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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
In music, a '''stacked chord''' is a set of well-defined pitches sounding together consisting of a stack of varying [[qualities]] of the same [[interval class]]. The most common stacked chords comprise of splitting a [[3/2]] or perfect fifth into two varying sizes of thirds. Stacked chords must be at least [[triad]]ic as dyadic can only contain one [[interval]].
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:kentaku|kentaku]] and made on <tt>2013-09-13 10:29:19 UTC</tt>.<br>
: The original revision id was <tt>450883782</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">In Music, &lt;span class="adtext"&gt;stacked&lt;/span&gt; chords are a set of well-&lt;span class="adtext"&gt;defined&lt;/span&gt; pitches sounding together consisting of a stack of varying flavors or qualities of the same numerical interval. The most common stacked chords comprise of splitting a 3/2 or perfect fifth into two varying sizes of thirds. Stacked chords must be at least triadic as dyadic can only contain on interval.


==5-limit tertiary harmonic triads==  
== 5-limit tertiary harmonic triads ==
{| class="wikitable"
|-
! Name
! Divides interval
! Chord formula
! Odd limit
|-
| Major
| 3/2
| 5/4 + 6/5 or M3 + m3
| 5
|-
| Minor
| 3/2
| 6/5 + 5/4 or m3 + M3
| 5
|-
| Augmented
| [[25/16]]
| 5/4 + 5/4 or M3 + M3
| 25
|-
| Diminished
| [[25/18]]
| 6/5 + 6/5 or m3 + m3
| 25
|}


|| **Name** || **Divides interval** || **Chord Formula** || **Odd Limit** ||
== 7-limit tertiary harmonic triads ==
|| &lt;span class="adtext"&gt;Major&lt;/span&gt; || 3/2 || 5/4 + 6/5 or M3 + m3 || 5 ||
{| class="wikitable"
|| Minor || 3/2 || 6/5 + 5/4 or m3 + M3 || 5 ||
|-
|| Augmented || 25/16 || 5/4 + 5/4 or M3 + M3 || 25 ||
! Name
|| &lt;span class="adtext"&gt;Diminished&lt;/span&gt; || 25/18 || 6/5 + 6/5 or m3 + m3 || 25 ||
! Divides interval
==5-limit tertiary harmonic tetrads==
! Chord formula
! Odd limit
|-
| Septimal (super)major
| 3/2
| [[9/7]] + 7/6 or 7M3 + 7m3
| 9
|-
| Septimal (sub)minor
| 3/2
| [[7/6]] + 9/7 or 7m3 + 7M3
| 9
|-
| [[Marvel]]-tempered augmented
| 14/9
| 5/4 + 5/4 or M3 + M3
| 9
|-
| [[Starling]]-tempered diminished
| 12/7
| 6/5 + 6/5 or m3 + m3
| 9
|}


|| **Name** || **Divides interval** || **Chord Formula** || **Odd Limit** ||
== 11-limit tertiary harmonic triads ==
|| &lt;span class="adtext"&gt;Major&lt;/span&gt; || 3/2 || 5/4 + 6/5 or M3 + m3 || 5 ||
{| class="wikitable"
|| Minor || 3/2 || 6/5 + 5/4 or m3 + M3 || 5 ||
|-
|| Augmented || 25/16 || 5/4 + 5/4 or M3 + M3 || 25 ||
! Name
|| &lt;span class="adtext"&gt;Diminished&lt;/span&gt; || 25/18 || 6/5 + 6/5 or m3 + m3 || 25 ||
! Divides interval
! Chord formula
! Odd limit
|-
| Neutral
| 3/2
| [[11/9]] + 11/9
| 11
|-
| 7:9:11
| 11/7
| 9/7 + 11/9 or SM3 + N3
| 11
|}


 
[[Category:Chord]]
==7-limit tertiary harmonic triads==
[[Category:todo:link]]
 
|| **&lt;span style="line-height: 1.5;"&gt;Name&lt;/span&gt;** || **&lt;span style="line-height: 1.5;"&gt;Divides interval&lt;/span&gt;** || **Chord Formula** || **Odd Limit** ||
|| Septimal Major || 3/2 || 9/7 + 7/6 or 7M3 + 7m3 || 9 ||
|| Septimal Minor || 3/2 || 7/6 + 9/7 or 7m3 + 7M3 || 9 ||
||  ||  ||  ||  ||
||  ||  ||  ||  ||
==11-limit tertiary harmonic triads==
 
|| **&lt;span style="line-height: 1.5;"&gt;Name&lt;/span&gt;** || **&lt;span style="line-height: 1.5;"&gt;Divides interval&lt;/span&gt;** || **Chord Formula** || **Odd Limit** ||
|| Neutral || 3/2 || 11/9 + 11/9 || 11 ||
||  ||  ||  ||  ||</pre></div>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Stacked Chords&lt;/title&gt;&lt;/head&gt;&lt;body&gt;In Music, &lt;span class="adtext"&gt;stacked&lt;/span&gt; chords are a set of well-&lt;span class="adtext"&gt;defined&lt;/span&gt; pitches sounding together consisting of a stack of varying flavors or qualities of the same numerical interval. The most common stacked chords comprise of splitting a 3/2 or perfect fifth into two varying sizes of thirds. Stacked chords must be at least triadic as dyadic can only contain on interval.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-5-limit tertiary harmonic triads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;5-limit tertiary harmonic triads&lt;/h2&gt;
&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;Name&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;Divides interval&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;Chord Formula&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;Odd Limit&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;span class="adtext"&gt;Major&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/4 + 6/5 or M3 + m3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Minor&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6/5 + 5/4 or m3 + M3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Augmented&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;25/16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/4 + 5/4 or M3 + M3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;span class="adtext"&gt;Diminished&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;25/18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6/5 + 6/5 or m3 + m3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-5-limit tertiary harmonic tetrads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;5-limit tertiary harmonic tetrads&lt;/h2&gt;
&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;Name&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;Divides interval&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;Chord Formula&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;Odd Limit&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;span class="adtext"&gt;Major&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/4 + 6/5 or M3 + m3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Minor&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6/5 + 5/4 or m3 + M3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Augmented&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;25/16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/4 + 5/4 or M3 + M3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;span class="adtext"&gt;Diminished&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;25/18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6/5 + 6/5 or m3 + m3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-7-limit tertiary harmonic triads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;7-limit tertiary harmonic triads&lt;/h2&gt;
&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;span style="line-height: 1.5;"&gt;Name&lt;/span&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;&lt;span style="line-height: 1.5;"&gt;Divides interval&lt;/span&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;Chord Formula&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;Odd Limit&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Septimal Major&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/7 + 7/6 or 7M3 + 7m3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Septimal Minor&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/6 + 9/7 or 7m3 + 7M3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x-11-limit tertiary harmonic triads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;11-limit tertiary harmonic triads&lt;/h2&gt;
&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;span style="line-height: 1.5;"&gt;Name&lt;/span&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;&lt;span style="line-height: 1.5;"&gt;Divides interval&lt;/span&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;Chord Formula&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;Odd Limit&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Neutral&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/9 + 11/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 14:25, 23 January 2025

In music, a stacked chord is a set of well-defined pitches sounding together consisting of a stack of varying qualities of the same interval class. The most common stacked chords comprise of splitting a 3/2 or perfect fifth into two varying sizes of thirds. Stacked chords must be at least triadic as dyadic can only contain one interval.

5-limit tertiary harmonic triads

Name Divides interval Chord formula Odd limit
Major 3/2 5/4 + 6/5 or M3 + m3 5
Minor 3/2 6/5 + 5/4 or m3 + M3 5
Augmented 25/16 5/4 + 5/4 or M3 + M3 25
Diminished 25/18 6/5 + 6/5 or m3 + m3 25

7-limit tertiary harmonic triads

Name Divides interval Chord formula Odd limit
Septimal (super)major 3/2 9/7 + 7/6 or 7M3 + 7m3 9
Septimal (sub)minor 3/2 7/6 + 9/7 or 7m3 + 7M3 9
Marvel-tempered augmented 14/9 5/4 + 5/4 or M3 + M3 9
Starling-tempered diminished 12/7 6/5 + 6/5 or m3 + m3 9

11-limit tertiary harmonic triads

Name Divides interval Chord formula Odd limit
Neutral 3/2 11/9 + 11/9 11
7:9:11 11/7 9/7 + 11/9 or SM3 + N3 11
Retrieved from "https://en.xen.wiki/index.php?title=Stacked_chord&oldid=177795"